The invention generally relates to fault protection of power transformers, and more specifically, to providing appropriate restraint for the main differential protection function during magnetizing inrush conditions.
Power transformers belong to a class of vital and very expensive components in electric power systems. If a power transformer encounters an internal short-circuit, it becomes necessary to take the transformer out of service within milliseconds so that the damage to the transformer and the surrounding system is minimized. Accordingly, high demands are imposed on power transformer protective relays. The requirements include dependability (no missing operations), security (no false trippings), and speed of operation (short fault clearing time).
A differential principle is commonly applied for protection of medium and large power transformers. A differential current is formed out of the terminal currents of a protected transformer using an external circuit (analog relays) or by the protective relay itself (microprocessor-based relays) in such a way that the differential current reflects an internal fault current. The differential current is close to zero when the protected transformer is sound and increases dramatically during internal faults.
Practically, the differential current may not be perfectly zero during normal operation of a power transformer due to certain factors such as limited accuracy of Current Transformers (CTs) used to measure the primary currents, operation of an on-load tap changer, or saturation of the CTs during external faults. To overcome this difficulty the stabilized (biased or percentage) differential principle is used which compares the differential current against a reference (restraint or stabilizing) current rather than against a fixed threshold. The restraint signal is created to reflect external fault currents.
Important issues related to differential protection of three-phase power transformers include phase angle and ratio matching, compensation for the ratio mismatch caused by operation of an on-load tap changer, CT saturation during external faults, and stationary overexcitation of the core (over-fluxing).
A separate issue of concern is a spurious differential current occurring when the core of the protected transformer is magnetized.
Magnetizing inrush current in power transformers results from any abrupt change of the transformer""s terminal voltage. Although usually considered a result of energizing a transformer, the magnetizing inrush may be caused by other factors such as occurrence of an external fault, voltage recovery after clearing an external fault, change of the character of a fault (evolving faults), and out-of-phase synchronizing of a connected generator.
Since the magnetizing branch representing the core of a transformer appears as a shunt element in the transformer equivalent circuit, the magnetizing current upsets the balance between the currents at the transformer terminals, and is therefore experienced by the differential relay as a spurious differential current threatening malfunction of the relay.
Initial magnetizing due to switching a transformer on is generally considered to cause the most severe case of an inrush. When a transformer is de-energized (switched-off), the magnetizing voltage is taken away, the magnetizing current goes to zero while the flux follows the hysteresis loop of the core. This results in certain remanent flux left in the core. When, afterwards, the transformer is re-energized by an alternating sinusoidal voltage, the flux becomes also sinusoidal but it is biased by the remanence. The residual flux may be as high as 80-90% of the rated flux, and therefore, it may shift the flux-current trajectories far above the knee-point of the characteristic resulting in saturation of the core, and consequently, large peak values and heavy distortions of the magnetizing current.
A typical waveform of the magnetizing inrush current contains a large and long lasting dc component, is rich in harmonics, has large peak values at the beginning, and decays substantially after a few tenths of a second, though a full decay occurs only after several seconds. The shape, magnitude and duration of the inrush current depend on several factors. The major ones include the rated power of the transformer, the short-circuit capability of the system from which the transformer is energized, the magnetic properties of the core, the remanence in the core, the moment and way the transformer is switched on.
Typical magnetizing inrush current is rich in harmonics with the second harmonic predominating. The minimum content of the second harmonic depends mainly on the knee-point of the magnetizing characteristic of the core. The lower the saturation flux density, the higher the amount of the second harmonic. Modern transformers built with improved magnetic materials have high knee-points, and therefore, their inrush currents contain comparatively low amounts of the second harmonic.
Modern methods of restraining differential relays rely on discriminating magnetizing inrush and internal fault conditions either indirectly (analysis of the available terminal signals of a transformer) or directly (extra sensors installed within the tank of a transformer such as the method disclosed in U.S. Pat. No. 3,832,600).
Analysis of the traditionally available terminal signals is the most common approach and includes several solutions with the harmonic restraint predominating.
The harmonic restraint permits tripping if the harmonic content is low; it inhibits the relay if the harmonic content is high. Mathematically, regardless of the applied relay technology and particular filtering solution, the harmonic-based restraint can be written as follows:
TP=ICH less than xcex94ICDxe2x80x83xe2x80x83(1)
where:
TP Trip Permission flag from the magnetizing inrush detector,
ICH Combined Harmonic component in the differential current,
ICD Combined Differential current,
xcex94 threshold.
Condition (1) originates a whole family of circuits (analog relays) or algorithms (microprocessor-based relays) due to various approaches to the combined currents ICH and ICD.
In the most common approach the amplitude of the second harmonic in the differential current in a given phase is the combined harmonic signal, while the amplitude of the fundamental frequency component in the differential current in the same phase is used as the combined differential current.
Depending on exact formulae employed for the combined harmonic and differential signals, magnetic properties of the core, and the required security/dependability balance, the threshold xcex94 in (1) would be set at slightly different values. Generally, however, the parameter xcex94 is set at about 0.15-0.20 (15-20%).
The harmonic restraint may be further refined. The method disclosed in U.S. Pat. No. 4,402,028 uses both the harmonic restraint and a voltage change function. The voltage change function determines whether or not the differential element requires harmonic restraint supervision, preempting such supervision when it is not required, to enable faster trip decisions to be made by the differential function.
The harmonic restraint in general, regardless of the method of composing the harmonic and differential signals (type of pre-filtering, type of phasor estimation, per phase versus three-phase operation, cross-phase restraining), faces certain limitations.
The most weighty limitation is that in modern transformers the amount of higher harmonics in the magnetizing current may drop well below 10% (the second harmonic as low as 7%, while the total harmonic content at a level of less than 8%). Under such circumstances, the setting xcex94 in (1) would have to be adjusted significantly below some 10%. This would lead, however, to delayed operation of the relay if not to the failure to operate during internal faults when the currents may be polluted with harmonic due to saturation of the CTs.
Another group of restraint techniques relies on direct wave-shape analysis. There are basically two restraining methods of this kind.
The first approach analyzes if the differential current contains periodically repeating intervals of low and flat values (xe2x80x9cdwell-timexe2x80x9d approach). Such intervals are signatures of the magnetizing inrush and if detected, they inhibit the main differential function.
The two most consequential weaknesses of this approach are:
CTs, when saturated during inrush conditions (very likely due to the dc component in the current), change the shape of the waveform within the xe2x80x9cdwell-timexe2x80x9d intervals and may cause malfunction of the relay.
During severe internal faults, when the CTs saturate, the secondary currents may exhibit spurious xe2x80x9cdwell-timexe2x80x9d intervals jeopardizing dependability of the relay (failure to trip).
The second algorithm of this class analyses polarity (sign) of the peak values and the decaying rate of the inrush current. The relay would be restrained if the two consecutive peaks of the differential current are of the same polarity and are displaced by approximately half of the power system cycle. Ideally, this method needs three quarters of a cycle to distinguish between internal faults and inrush conditions.
Practically, however, this restraint principle has its limitations. In a three-phase transformer not always the differential currents are of the typical inrush shape in all three phases. Therefore, the three-phase transformer protection would need a kind of cross-phase restraint.
Another group of techniques suitable for microprocessor-based relays relies on solving on-line the mathematical model of a fault-free transformer. Either certain parameters of the model are computed assuming the measured signals; or certain fraction of the terminal variables are computed based on all the remaining signals, and next compared to their measured counterparts. In the first case such as in the method disclosed in U.S. Pat. No. 5,170,308, the values of the calculated parameters differentiate internal faults from other disturbances (including inrush conditions). In the second case such as in the method disclosed in U.S. Pat. No. 3,754,163, the difference between the calculated and measured signals enables the relay to perform the classification.
Another relaying principle uses the differential active power to discriminate between internal faults and other conditions (including magnetizing inrush). The operating signal is a difference between the instantaneous powers at all the terminals of a protected transformer.
Yet another restraining algorithm suitable for microprocessor-based relays differentiates internal faults from magnetizing inrush conditions using the flux in the transformer""s core estimated (calculated) on-line from the available terminal voltages and currents.
The known methods of dealing with the magnetizing inrush problem leave significant room for improvement. It would be desirable to improve security without jeopardizing dependability of the main differential function.
The present invention overcomes the disadvantages of known inrush restraining methods without jeopardizing the dependability of the transformer protection relay.
In the disclosed embodiments, an inrush restraining method responds to a complex second harmonic ratio.
In one embodiment, a Fourier series of the fundamental frequency component and higher harmonics represents the waveform of the differential current. The fundamental frequency component is a phasor rotating at the system radian frequency. The second harmonic component is a phasor rotating at exactly twice the system frequency. The traditional second harmonic restraint measures and uses the ratio of the magnitudes of the second harmonic and the fundamental component neglecting the phase angle information.
The present invention utilizes the phase angle relation between the fundamental component and the second harmonic in addition to the magnitude ratio. This is accomplished by calculating a complex second harmonic ratio, a complex number having a magnitude based on a traditional second harmonic ratio of the magnitudes, and an argument based on a phase angle between the fundamental frequency component and the second harmonic.
When the traditional second harmonic ratio drops below the usual threshold setting during magnetizing inrush conditions jeopardizing the security, the phase angle of the complex second harmonic ratio follows certain characteristic pattern. That pattern enables the differentiation between internal faults and magnetizing inrush cases.
Considering the differences between internal faults and magnetizing inrush conditions in both the magnitude and phase angle of the complex second harmonic ratio, an optimal operating characteristic has been defined as a part of this invention. The characteristic is dynamic: it changes in time providing more security when needed and enhancing dependability when possible.